Information decomposition in complex systems via machine learning

TL;DR

This paper introduces a machine learning-based method for decomposing information in complex systems, enabling the identification of variations most relevant to macro-level behavior, demonstrated on Boolean circuits and amorphous materials.

Contribution

It presents a practical information decomposition technique using the distributed information bottleneck, facilitating analysis of micro- and macro-scale relationships in complex systems.

Findings

Successfully decomposed system entropy into meaningful components

Applied method to Boolean circuits and amorphous materials

Identified variations most relevant to macroscale behavior

Abstract

One of the fundamental steps toward understanding a complex system is identifying variation at the scale of the system's components that is most relevant to behavior on a macroscopic scale. Mutual information provides a natural means of linking variation across scales of a system due to its independence of functional relationship between observables. However, characterizing the manner in which information is distributed across a set of observables is computationally challenging and generally infeasible beyond a handful of measurements. Here we propose a practical and general methodology that uses machine learning to decompose the information contained in a set of measurements by jointly optimizing a lossy compression of each measurement. Guided by the distributed information bottleneck as a learning objective, the information decomposition identifies the variation in the measurements of the system state most relevant to specified macroscale behavior. We focus our analysis on two paradigmatic complex systems: a Boolean circuit and an amorphous material undergoing plastic deformation. In both examples, the large amount of entropy of the system state is decomposed, bit by bit, in terms of what is most related to macroscale behavior. The identification of meaningful variation in data, with the full generality brought by information theory, is made practical for studying the connection between micro- and macroscale structure in complex systems.